Spin-orbital physics in the optical conductivity of quarter-

Using finite-temperature diagonalization we investigate the optical conductivity $\sigma(\omega)$ and spin-orbital dynamics in the CE phase of half-doped manganites. We find $\sigma(\omega)$ characterized by a broad spectrum with pronounced optical gap due

Spin-orbitalphysicsintheopticalconductivityofquarter- lledmanganites

JanBa la1,2andPeterHorsch1

2

Max-Planck-Institutf¨urFestk¨orperforschung,Heisenbergstrasse1,D-70569Stuttgart,Germany

MarianSmoluchowskiInstituteofPhysics,JagellonianUniversity,Reymonta4,PL-30059Krak´ow,Poland

(Dated:February2,2008)

Using nite-temperaturediagonalizationweinvestigatetheopticalconductivityσ(ω)andspin-orbitaldynamicsintheCEphaseofhalf-dopedmanganites.We ndσ(ω)characterizedbyabroadspectrumwithpronouncedopticalgapduetochargeorderinginducedbyCoulombandfurtherneighborJahn-Tellerinteractions.Withincreasingtemperaturetheconductivityshowsasigni cantchangeoverawideenergyrangewithacharacteristicshifttowardslowerfrequencies.InthelowtemperatureCEphaseweobservein-gapabsorptionduetocombinedorbiton-spinexcitations.

PACSnumbers:75.10.-b,71.70.Ej,75.30.Et,75.40.Mg

1

arXiv:cond-mat/0503011v1 [cond-mat.str-el] 1 Mar 2005

Thelargevariationofphysicalpropertiesofmangan-itesasfunctionofdopingortemperatureoriginatesfromacomplexinterplayofspin,orbitalandchargedegreesoffreedom,aswellastheinteractionwiththelattice2].AnimportantexampleforthecontrolofmagneticorderduetotheorbitaldegreeoffreedomistheCEphaseatquarter lling.Hereferromagnetic(FM)zig-zagchainsarestaggeredantiferromagneticallyandtheoccupiedegorbitalsareorientedalongFMbondsinthe(a,b)planes[3][Fig.1(a,b)].Althoughthestructurere ectsthecoop-erativeactionofantiferromagnetic(AF)superexchangeandFMdouble-exchange(DE),theseinteractionsalonedonotguaranteeitsstability[4,5].TheAF-CEphasewasobservedincubic(Nd,Pr)1/2(Sr,Ca)1/2MnO3andinlayeredLa1/2Sr3/2MnO4LaSr2Mn2O7man-ganites.YetCE-typeorbitalcorrelationshavealsobeenobservedintheabsenceofantiferromagnetism,namelyintheFMmetallicphaseofNd1/2Sr1/2MnO3andalsoatsmallerholedopingandarebelievedtobeconnectedwiththemechanismofcolossalmagnetoresistanceAnimportantfeatureoftheCE-phaseisalargeopticalgapandabroadabsorptionmaximumat1–2eVshiftingtowardslowerfrequencieswithincreasingtemperature[11,12,13].Remarkablyasimilarspectralshiftisob-servedinphoto-excitationexperiments,whichrevealul-trafastresponsetimesofsuchMottinsulatingstructures[2,14].

Ouraimistoinvestigatetheelectrondynamics(opti-calconductivity,elementaryexcitations)intheCEspin-orbitalstate.Itisevidentthatarealunderstandingofthisphaseisonlyachievedifalsotheexcitationspec-traareconsistentwithexperiment.Thestrongvariationofσ(ω)withtemperatureTwasnotaddressedinprevi-oustheoreticalwork[15,16].Ourstudyemploying nitetemperaturediagonalizationisdesignedtoexplorealsoquantities,suchastheorbitalexcitationspectra,thatsofarcannotbemeasuredbyexperimentandinvestigatetheire ectonobservableslikeopticalconductivityandspinexcitations.Ourresultsfortheopticalconductivityreproduceforthe rsttimetheexperimentaltrendsonasemi-quantitativelevel,andpredictorbitalexcitations

inthechargegapoftheAF-CEphase.

Orbitaldegeneracyprovidestheoptionforthesystemtoloweritsdimensionality,whichisessentialfortheap-pearanceoftheCEstructureOurstudyexploresanovelaspectoforbitalphysicsinmanganites,namelytheroleoffurtherneighborJahn-Teller(JT)interactions,andtheconsequencesonthedynamics.We ndthator-bitalpolarizationinducedbythisinteractioniscrucialfortheappearanceofCE-antiferromagnetismatlowT,andleadstoaspinresponseconsistentwithAF-CEorder.WeconsideranextendedDEmodelwithchargeor-der(CO)triggeredbyCoulombrepulsionandfurther-neighborJT-interaction[5].AForderalongthecaxisandegorbitalelongationinthea/bdirectioncon nestheelectrondynamicsto(a,b)planesandthuswecon-sideratwo-dimensional(2D)model.Assumingin niteon-siteCoulombrepulsionbetweenegelectronsonthesamesite(U→∞)themodelhastheform ξζ

H= Sctijdiξσdjζσ+H.c. JHi·si

ij ξζ,σ

+JAF

ij

cSci·Sj+V

ij

i

ninj+HOO.(1)

The rsttermdescribesthemotionofegelectronsun-dertheconstraintthateachsitecanbeoccupiedatmost =d(1 niξσbyoneegelectron,d¯′).¯)σ′(1 niξσiξσiξσ¯(¯Heretheindexξσ)denotestheegorbital(spin)orthog-onaltoξ(σ),respectively.Thehoppingmatrixelements

22

tξζijintheorbitalbasis{|x ,|z }with|x ～x yand|z ～3z2 r2havethestandardform[18].Thesec-ondterminstandsforHund’scouplingbetween

electronspinsi=ξσσ′diξσσσσ′diξσ′andthet2gcore

c

spinSci(S=3/2).ThethirdtermrepresentstheAFsuperexchange(JAF>0)betweennearest-neighbort2gspins,whilethefourthtermistheinter-siteCoulombre-pulsionwhichfavorscheckerboardCO(V>0).Finally

HOO=2κ

′

jij′

(1 ni)Tjj′,(2)